Logical operations

T (logical; physical T-dagger on every qubit) transversal claimed

Level: non-Clifford (Clifford hierarchy level 3) · Cost: one parallel physical-T-dagger layer in the constructor's explicit logical basis

References: bravyihaah2012magic

CNOT transversal claimed

Level: Clifford · Cost: one pairwise physical-CNOT layer between aligned blocks; routing is additional

References: paetznick2013universal

H switching claimed

Level: Clifford · Cost: convert to Steane, apply its transversal H, and convert back; syndrome extraction and conditional correction are part of both conversions

References: anderson2014conversion

15-to-1 T-state distillation measurement-based claimed

Level: non-Clifford resource protocol · Cost: fifteen noisy inputs, one Reed–Muller parity check, decoding, and acceptance-conditioned output; circuit overhead depends on the factory realization

References: bravyi2005magic